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Question
The temperature of a uniform rod of length L having a coefficient of linear expansion αL is changed by ∆T. Calculate the new moment of inertia of the uniform rod about the axis passing through its center and perpendicular to an axis of the rod.
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Solution
Moment of inertia of a uniform rod of mass and length l about its perpendicular bisector. Moment of inertia of the rod
I = `1/12"ML"^2`
Increase in length of the rod when temperature is increased by ∆T, is given by
L’ = L(1 + αL∆T)
I’ = `"ML’"^2/12 = "M"/12"L"^2`(1 + αL∆T)2
I’ = I(1 + αL∆T)2
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